A current carrying circular loop is perpendicular to a magnetic field of induction `10^(-4) ` T . If the radius of the loop starts shrinking at a uniform rate of 2 `mms^(-1)` then the emf induced in the loop at the instant when its radius is 20 cm will be

Options

A. 0.02 `pimuV `
B. `0.08 pimuV`
C. `0.03 pimuV `
D. `0.05 pimuV`

Answer

B

Explanation

Given B = `10^(-4)T r = 20 cm = 20xx10^(-2)` m
`(dr)/(dt)= -(2mm)/(s)= -2xx10^(-3)(m)/(s)`
Induced emf `epsi = - (dphi)/(dt) implies epsi=- (d)/(dt)(B.pir^(2))`
`epsi = - Bpi. (dr^(2))/(dt)= -Bpi (2r. (dr)/(dt))`
`epsi= 10^(-4)xxpixx2xx20xx10^(-2)xx2xx10^(-3)`
`epsi = 8pixx10^(-8) = 0.08 pi (muV)`